(a) The spread of an oil slick of depth Z and density ρ O is to be stopped by a floating boom, as shown in The boom, which is designed to float upright as shown in the figure, has a square cross...

(a) The spread of an oil slick of depth Z and density ρ_O
is to be stopped by a floating boom, as shown in The boom, which is designed to float upright as shown in the figure, has a square cross section of side t and weight per unit length w. Show that the maximum slick depth ZMAX which can be contained by the boom is given by

where ρS is the density of the sea water beneath the slick and g is the acceleration due to gravity.

(b) Calculate the horizontal force per unit length acting on the water side of the boom if t is 500 mm, w is 2300 N/m, and the relative density of sea water is 1.025. Also calculate the depth below the top surface of the boom at which the horizontal force acts. Would the horizontal force on the oil side of the boom be greater or smaller than that on the water side? Give a brief explanation for your answer.